Find the power series for the function $f ( x ) = \frac { 8 x } { x + 1 }$ using the power series for $\frac { 1 } { x + 1 }$ .
A) $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n + 1 } 8 x ^ { n + 1 }$
B) $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } 8 x ^ { n - 1 }$
C) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } 8 x ^ { n - 1 }$
D) $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } 8 x ^ { n + 1 }$
E) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } 8 x ^ { n + 1 }$

Question

Quizplus · Accepted Answer

The power series for $\frac{1}{x+1}$ is $\sum_{n=0}^{\infty} (-1)^n x^n$. Multiplying by $8x$ gives $\sum_{n=0}^{\infty} (-1)^n 8x^{n+1}$.

Find the Power Series for the Function f(x)=8xx+1f ( x ) = \frac { 8 x } { x + 1 }f(x)=x+18x​

Find the Power Series for the Function $f ( x ) = \frac { 8 x } { x + 1 }$